1. **State the problem:** We are given that the product of two numbers is $-\frac{28}{27}$ and one of the numbers is $-\frac{4}{9}$. We need to find the other number. 2. **Formula used:** If the product of two numbers $a$ and $b$ is $P$, then $a \times b = P$. To find $b$, we use the formula: $$ b = \frac{P}{a} $$ 3. **Apply the formula:** Here, $P = -\frac{28}{27}$ and $a = -\frac{4}{9}$. Substitute these values: $$ b = \frac{-\frac{28}{27}}{-\frac{4}{9}} $$ 4. **Simplify the division of fractions:** Dividing by a fraction is the same as multiplying by its reciprocal: $$ b = -\frac{28}{27} \times -\frac{9}{4} $$ 5. **Multiply the numerators and denominators:** $$ b = \frac{(-28) \times (-9)}{27 \times 4} = \frac{252}{108} $$ 6. **Simplify the fraction:** Both numerator and denominator can be divided by 12: $$ b = \frac{252 \div 12}{108 \div 12} = \frac{21}{9} $$ 7. **Further simplify:** Both numerator and denominator can be divided by 3: $$ b = \frac{21 \div 3}{9 \div 3} = \frac{7}{3} $$ **Final answer:** The other number is $\boxed{\frac{7}{3}}$.